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arXiv:2505.24300 · Physical review. B./Physical review. B

Probing quasiparticle excitations in a doped Mott insulator via Friedel oscillations

Anurag Banerjee, Emile Pangburn, C. Pépin, Cristina Bena B

Published Sep 15, 2025• 0 citations
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Abstract

In this work, we investigate impurity-induced Friedel oscillations in the doped two-dimensional Hubbard model, focusing on the role of holon and doublon excitations. We show that weak impurities, due to the non-fermionic nature of the underlying quasiparticles, induce Friedel oscillations whose behavior is consistent with an effective non-interacting theory for these quasiparticles, and whose wavevector reflects the violation of Luttinger's theorem. At larger impurity strength, the system transitions to a phase-separated state composed of coexisting Mott-insulating (half-filled) and hole-rich regions. Within the composite operator framework, this phase separation arises from a competition between the kinetic energy of holons and the tendency to form tightly bound holon-doublon pairs. Our results offer new insights into the nature of charge carriers and the emergent electronic phases in the doped Mott regime.

DOI
10.1103/fbq7-792q

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In this work, we investigate impurity-induced Friedel oscillations in the doped two-dimensional Hubbard model, focusing on the role of holon and doublon excitations. We show that weak impurities, due to the non-fermionic nature of the underlying quasiparticles, induce Friedel oscillations whose behavior is consistent with an effective non-interacting theory for these quasiparticles, and whose wavevector reflects the violation of Luttinger's theorem. At larger impurity strength, the system transitions to a phase-separated state composed of coexisting Mott-insulating (half-filled) and hole-rich regions. Within the composite operator framework, this phase separation arises from a competition between the kinetic energy of holons and the tendency to form tightly bound holon-doublon pairs. Our results offer new insights into the nature of charge carriers and the emergent electronic phases in the doped Mott regime.
Luttinger's theorem has long been taken as the key feature of Landau's Fermi liquid, which signals the presence of quasiparticles. Here, by the unbiased Monte Carlo method, violation of Luttinger's theorem is clearly revealed in the Falicov-Kimball (FK) model, indicating a robust correlation-driven non-Fermi-liquid characteristic under any electron density. Introducing hole carriers to the half-filled FK model leads to Mott insulator-metal transition, where the Mott quantum criticality manifests unconventional scaling behavior in transport properties. Further insight on the violation of Luttinger's theorem is examined by combining Hubbard-I approximation with a composite fermion picture, which emphasizes the importance of a mixed excitation of the itinerant electron and the composite fermion. Interestingly, comparing the FK model with a binary disorder system suggests that the two-peak band structure discovered by Monte Carlo and Hubbard-I approaches is underlying the violation of Luttinger's theorem.
Electronic correlations arise from the competition between the electrons' kinetic and Coulomb interaction energy and give rise to a rich phase diagram and many emergent quasiparticles. The binding of doubly-occupied and empty sites into a doublon-holon exciton is an example of this in the Hubbard model. Unlike traditional excitons in semiconductors, in the Hubbard model it is the kinetic energy which provides the binding energy. Upon doping, we find the emergence of exciton complexes, such as a holon-doublon-holon trion. The appearance of these low-lying collective excitations make screening more effective in the doped system. As a result, Hubbard-based modelling of correlated materials should use different values of UUU for the doped system and the insulating parent compound, which we illustrate using the cuprates as an example.
We argue that the binding between doubly occupied (doublon) and empty (holon) sites governs incoherent excitations and plays a key role in the Mott transition in strongly correlated Mott-Hubbard systems. We construct a new saddle-point solution with doublon-holon binding in the Kotliar-Ruckenstein slave-boson functional integral formulation of the Hubbard model. On a half-filled honeycomb lattice and square lattice, the ground state is found to exhibit a continuous transition from a paramagnetic semimetal/metal to an antiferromagnetic-ordered Slater insulator with coherent quasiparticles at Uc1{U}_{c1}Uc1​, followed by a Mott transition into an electron-fractionalized AF∗{}^{*}∗ phase without coherent excitations at Uc2{U}_{c2}Uc2​. Such a phase structure appears to be generic for bipartite lattices without frustration. We show that doublon-holon binding unites the three important ideas of strong correlation: coherent quasiparticles, incoherent Hubbard bands, and deconfined Mott insulator.
Experimental studies reveal a striking asymmetry in low-energy single-particle excitations between electron- and hole-doped cuprates. Electron-doped cuprates display a nontrivial dichotomy: Fermi-liquid-like behavior (suggesting weaker electronic correlations) coexists with correlation-driven features typical of hole-doped systems. This dual nature challenges a unified description within a doped Mott insulator framework. The present work addresses this issue by establishing that the ground-state wave function of the ttt-t′t't′-JJJ model generically possesses a two-component structure, comprising a coherent quasiparticle and an incoherent composite component. The kinetic energy arises from both the intrinsic propagation of the coherent quasiparticle and the resonance between these components. Using variational Monte Carlo at the level of a single hole, we show that for hole doping (t′<0t'<0t′<0), this resonance between components dominates and concentrates in the nodal region at low energies. This emergent propagation induced by resonance can be physically interpreted as originating from the recombination of fractionalized degrees of freedom, which drives various phenomena associated with strong correlations. Conversely, for electron doping (t′>0t'>0t′>0), the coherent quasiparticle propagation, which exhibits conventional properties of a Fermi liquid, is selectively enhanced in the antinodal region at low energies. This produces a separation in momentum space for systems with electron doping: the antinodal spectral weight at low energies is governed by the coherent quasiparticle, fundamentally differing from the nodal region, which remains dominated by the incoherent composite component. Motivated by such a structure and guided by experimental observations, we propose a phenomenological Green's function at finite doping, yielding spectral features consistent with experiments.
We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon–doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon–doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott–Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.
Though most fermionic Mott insulators order at low temperatures, ordering is ancillary to their insulating behavior. Our emphasis here is on disentangling ordering from the intrinsic strongly correlated physics of a doped half-filled band. To this end, we focus on the two-dimensional Hubbard model. Because the charge gap arises from on-site correlations, we have been refining the nonperturbative approach of Matsumoto and Mancini [Phys. Rev. B 55, 2095 (1997)] which incorporates local physics. Crucial to this method is a self-consistent two-site dynamical cluster expansion which builds in the nearest-neighbor energy scale J. At half-filling, we find that the spectral function possesses a gap of order U and is devoid of any coherent quasiparticle peaks although ordering or charge fractionalization are absent. At low temperatures, local antiferromagnetic correlations emerge. In the doped case, we find that the Fermi surface exceeds the Luttinger volume. The breakdown of Luttinger's theorem in the underdoped regime is traced both to the dynamically generated Mott gap as well to a nonvanishing of the imaginary part of the self-energy at the Fermi level. Spectral weight transfer across the Mott gap also emerges as a ubiquitous feature of a doped Mott insulator and suggests that high- and low-energy scales are inseparable. Additionally in the underdoped regime, we find that a pseudogap exists in the single-particle density of states as well as in the heat capacity. The pseudogap (which is set by the energy scale t2/U){t}^{2}/U)t2/U) is argued to be a ubiquitous feature of a lightly doped Mott state and simply represents the fact that hole transport involves double occupancy. In analogy with the Mott gap and antiferromagnetism, we propose that ordering may also accompany the formation of a pseudogap. We suggest a current pattern within a one-band model that preserves translational but breaks time-reversal symmetry along the canonical x and y axes but not along $x=\ifmmode\pm\else\textpm\fi{}y$ that is consistent with the experimental observations. Finally, we show that the Hall coefficient in a doped Mott insulator must change sign at a doping level x<1/3.x<1/3.x<1/3. The sign change is tied to a termination of strong correlation physics in the doped Mott state.